Negative Binary Numbers

1
Negative Binary Numbers
2
Ummm...

• Computers can only use 1s and 0s
• How do we represent a negative number?

3
Sign Magnitude

• Use the Most Significant Bit (MSB) as a sign bit
  to indicate the sign of a number
• MSB is the bit on the farthest left
• Commonly refered as Sign Magnitude
• 0 (on far left) positive number
• 1 (on far left) negative number
• Example 00102 210 10102 -210
• 0101012 21 1101012 -2110

4
Sign Magnitude Maximum Value

• Maximum value is now different because we use one
  of the bits to indicate the sign!
• Given N bits and using the sign magnitude system,
  what is the biggest possible number (maximum
  value)?

5
Sign Magnitude Minimum Value

• Without the sign bit, our minimum value was 0
• Minimum value is now different because we have
  negative numbers
• Given N bits and using the sign magnitude system,
  what is the lowest possible number (minimum
  value)?

6
Minimum/Maximum Value Example

• Given 4 bits in the sign magnitude system
• Maximum 24 - 1 1 7
• Minimum - (24 - 1 1) -7
• How many different numbers can we represent with
  4 bits?

7
Oh, no!

• There is an inherent problem with using a sign
  bit
• HINT
• What is 0000 in sign magnitude?
• What is 1000?